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Консультация № 199617
16.11.2020, 04:01
0.00 руб.
1
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Исследовать на сходимость ряд:
По признаку Даламбера получилось 1, онлайн-калькулятор говорит, что ряд сходится по сравнительному признаку.
Исследовать на сходимость ряд:
По признаку Даламбера получилось 1, онлайн-калькулятор говорит, что ряд сходится по сравнительному признаку.
Прикрепленные файлы:
Обсуждение
20.11.2020, 19:14
общий
это ответ
Здравствуйте, lyskov.kirill!
Воспользуемся интегральным признаком сходимости: если имеется непрерывная убывающая функция f(x) и последовательность a[sub]n[/sub] = f(n), n=1,2,3,..., то ряд
и интеграл
одновременно сходятся, либо расходятся. В данном случае для f(x) = 1/[$8730$]x[sup]3[/sup] интеграл
сходится, поэтому одновременно сходится ряд
и поскольку
для всех n, то ряд
также сходится (по признаку сравнения рядов).
Воспользуемся интегральным признаком сходимости: если имеется непрерывная убывающая функция f(x) и последовательность a[sub]n[/sub] = f(n), n=1,2,3,..., то ряд
и интеграл
одновременно сходятся, либо расходятся. В данном случае для f(x) = 1/[$8730$]x[sup]3[/sup] интеграл
сходится, поэтому одновременно сходится ряд
и поскольку
для всех n, то ряд
также сходится (по признаку сравнения рядов).
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